
simplex algorithm
i'm just really confused by the way simplex algorithm works. this problem im working on asks to carry out two iterations to the following problem:
minimize f(x)=2x1+3x2 subject to the following constraints:
x1>=1
x2<=1+x1
x1+x2<=3
x2<=2
x2>=1
denote the feasible solution S.
so first question i have about this problem is, how do i form the index set? none of the sources i read explain clearly how to do it.

sorry for the question. i found out there is a degenerate vertex point which means that the simplex method does not apply. but does someone know a good site where i can get a good tutorial for the simplex method? it seems like many tutorials or books are confusing to understand. thanks.